Operator Precedence (How Operators Nest)
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   "Operator precedence" determines how operators are grouped, when
different operators appear close by in one expression.  For example,
`*' has higher precedence than `+'; thus, `a + b * c' means to multiply
`b' and `c', and then add `a' to the product (i.e., `a + (b * c)').

   You can overrule the precedence of the operators by using
parentheses.  You can think of the precedence rules as saying where the
parentheses are assumed if you do not write parentheses yourself.  In
fact, it is wise to always use parentheses whenever you have an unusual
combination of operators, because other people who read the program may
not remember what the precedence is in this case.  You might forget,
too; then you could make a mistake.  Explicit parentheses will help
prevent any such mistake.

   When operators of equal precedence are used together, the leftmost
operator groups first, except for the assignment, conditional and
exponentiation operators, which group in the opposite order.  Thus, `a
- b + c' groups as `(a - b) + c'; `a = b = c' groups as `a = (b = c)'.

   The precedence of prefix unary operators does not matter as long as
only unary operators are involved, because there is only one way to
parse them--innermost first.  Thus, `$++i' means `$(++i)' and `++$x'
means `++($x)'.  However, when another operator follows the operand,
then the precedence of the unary operators can matter.  Thus, `$x^2'
means `($x)^2', but `-x^2' means `-(x^2)', because `-' has lower
precedence than `^' while `$' has higher precedence.

   Here is a table of the operators of `awk', in order of increasing
precedence:

assignment
     `=', `+=', `-=', `*=', `/=', `%=', `^=', `**='.  These operators
     group right-to-left.  (The `**=' operator is not specified by
     POSIX.)

conditional
     `?:'.  This operator groups right-to-left.

logical "or".
     `||'.

logical "and".
     `&&'.

array membership
     `in'.

matching
     `~', `!~'.

relational, and redirection
     The relational operators and the redirections have the same
     precedence level.  Characters such as `>' serve both as
     relationals and as redirections; the context distinguishes between
     the two meanings.

     The relational operators are `<', `<=', `==', `!=', `>=' and `>'.

     The I/O redirection operators are `<', `>', `>>' and `|'.

     Note that I/O redirection operators in `print' and `printf'
     statements belong to the statement level, not to expressions.  The
     redirection does not produce an expression which could be the
     operand of another operator.  As a result, it does not make sense
     to use a redirection operator near another operator of lower
     precedence, without parentheses.  Such combinations, for example
     `print foo > a ? b : c', result in syntax errors.

concatenation
     No special token is used to indicate concatenation.  The operands
     are simply written side by side.

add, subtract
     `+', `-'.

multiply, divide, mod
     `*', `/', `%'.

unary plus, minus, "not"
     `+', `-', `!'.

exponentiation
     `^', `**'.  These operators group right-to-left.  (The `**'
     operator is not specified by POSIX.)

increment, decrement
     `++', `--'.

field
     `$'.